An AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. Figures 1-4 illustrate the rotation rules.

Now given a sequence of insertions, you are supposed to tell the root of the resulting AVL tree.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer N (<=20) which is the total number of keys to be inserted. Then N distinct integer keys are given in the next line. All the numbers in a line are separated by a space.

Output Specification:

For each test case, print ythe root of the resulting AVL tree in one line.

Sample Input 1:

5
88 70 61 96 120

Sample Output 1:

70

Sample Input 2:

7
88 70 61 96 120 90 65

Sample Output 2:

88

给定条件：
1.n个节点

要求：
1.用这n个节点建立平衡二叉搜索树，并且输出根节点的值

求解：
1.裸的AVL，建议搜索相关知识进行学习。思路全部都一样，不一样的是你手下的代码,（你喜欢哪种风格？）:p
2.以下给出参考代码:

#include<cstdio>
#define max(a,b) ((a) > (b) ? (a) : (b))
struct node {
	int val;
	node *left, *right;
};

node *LL(node *root){
	node *t = root->left;
	root->left = t->right;
	t->right = root;
	return t;
}
node *RR(node *root){
	node *t = root->right;
	root->right = t->left;
	t->left = root;
	return t;
}
node *LR(node *root){
	root->left = RR(root->left);
	return LL(root);
}

node *RL(node *root){
	root->right = LL(root->right);
	return RR(root);
}

int getHeight(node *root){
	if(root == nullptr) return 0;
	return max(getHeight(root->left), getHeight(root->right)) + 1;
	return 1;
}

node *insert(node *root, int val){
	if(root == nullptr) {
		root = new node();
		root->val = val;
		root->left = root->right = nullptr;
	} else if(val < root->val) {
		root->left = insert(root->left, val);
		if(getHeight(root->left) - getHeight(root->right) == 2)
			root = val < root->left->val ? LL(root) : LR(root);
	} else {
		root->right = insert(root->right, val);
		if(getHeight(root->left) - getHeight(root->right) == -2)
			root = val > root->right->val ? RR(root) : RL(root);
	}
	return root;
}

int main(){
	int n, val;
	node *root = nullptr;
	scanf("%d", &n);
	for(int i = 0; i < n; i++) {
		scanf("%d",&val);
		root = insert(root, val);
	}
	printf("%d\n", root->val);
	return 0;
}